Abstract
Especially, land and sea surface temperature anomalies are considered important measures in assessing the state of climate change. Recent developments and accelerations of climate change, primarily driven by human influence, have caused a seemingly divergence in land and sea surface temperature anomalies. In this paper, we establish the initial grounds for testing whether a cointegrating relationship can cease to exist or have breaks. We motivate the cointegration by parts test using theory behind financial bubbles, and base our initial procedure on a recursive left-sided unit root test. Our preliminary testing framework is used in a simulation study in which we force a divergence in cointegration. After establishing the validity of our recursive test, we perform the analysis on land and sea surface temperature anomalies. Initially, we do not find evidence for a break in the cointegration between the two temperature anomaly series.